Function handle issue regarding Trig Fourier Series

T = 5; % period
w0 = 2*pi/T;

F = @(s) [10.*(0<=s & s<1) + 0.*(1<=s & s<=5)];

N = 1000; % 2*N+1 is number of terms in the sum
B = N/T; % The highest frequency is B=N/T
dt = 1/(3*B); % the Nyquist rate is 1/(2*B)

a0 = (1/T)*integral(F,0,T); % mean value over the period
An = zeros(N); phase = zeros(N); 

t = -6:dt:7; 

sum = a0*ones(size(t));
for n=1:N
   an = (2/T)*integral(F,0,T);     % Fourier coefficients
   bn = (2/T)*integral(F,0,T);     % Fourier coefficients
   sum = sum + an*cos(n*w0*t) + bn*sin(n*w0*t);
end

This is my code at the moment and im trying to calculate the an and bn values. The changed code below is what im trying to achieve but it will show up with an error.

an = (2/T)*integral(F*cos(n*w0*t),0,T);     % Fourier coefficients
bn = (2/T)*integral(F*sin(n*w0*t),0,T);     % Fourier coefficients

If i run it with this code, I get the error

"Operator '*' is not supported for operands of type 'function_handle'."

Any help would be appreciated.

Answer 1

[Star Strider]

In this situaiton, it is necessary to evaluate the function, and also use the 'ArrayValued' name-value pair:

for n=1:N
    an = (2/T)*integral(@(s)F(s).*cos(n.*w0.*t),0,T, 'ArrayValued',1);     % Fourier coefficients
    bn = (2/T)*integral(@(s)F(s).*sin(n.*w0.*t),0,T, 'ArrayValued',1);     % Fourier coefficients
   sum = sum + an.*cos(n.*w0.*t) + bn.*sin(n.*w0.*t);
end

It takes a few seconbds more to run, however it appears to produce an appropriate plot with:

figure
plot(t, sum)
grid

.